The Nonstationary Newsvendor: Data-Driven Nonparametric Learning

We study a newsvendor problem with unknown demand distribution in a nonstationary demand environment over a multiperiod time horizon. The demand in each period consists of a time-varying demand level and an additive random shock. Neither the demand level nor the random shock is separately observable. The amount of change in the demand level over the time horizon is measured by a cumulative variation metric. The problem has widespread applications, such as perishable inventory planning, staffing, and medical resource capacity planning in the wake of COVID-19. We design a family of nonparametric dynamic ordering policies, termed two-stage estimation (2SE) policies, that track the shifts in the unknown demand level while accounting for the unobservable random demand shocks. To compute the order quantity in each period, these policies only need the past demand observations, without any access to the underlying demand distribution. For a finite variation “budget,” we prove that our ordering policies are first-order optimal in the sense that their regret grows at the smallest possible rate. We also extend our analysis to the case of asymptotically large variation budgets. Through case studies based on real-life data, we show that our policies can save more than 20% of overage and underage costs, relative to policies widely used for perishable inventory replenishment and nurse staffing. Moreover, our simulation experiments indicate that our policies consistently maintain superior performance across diverse patterns of nonstationary demand environments.

This paper was accepted by David Simchi-Levi, operations management.

Funding: N. B. Keskin and J.-S. Song were supported by the Duke University Fuqua School of Business, and X. Min was supported by the National Natural Science Foundation of China [Grant 72401195] and the China Postdoctoral Science Foundation [2025T180216].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01823.